My mirror ball is not shading correctly - it looks too flat
The Look Dev mode uses an HDRI which produces the nice reflections in your first image. As the name suggests the Look Dev mode is only meant to develop the look of your model, not for a preview of the final render, that is what the Rendered mode is for. If you want to use the scene's world settings instead of the HDRI preset in Look Dev, you can enable Scene World in the Viewport Shading settings.



In order to use an HDRI in your render, you'll have to set it up in the world tab or its node editor.



Blender 2.80






Blender 2.81